Hi i know this is a really really simple question but it has me confused....

rastafarral6

rastafarral6

Answered question

2021-11-13

Hi i know this is a really really simple question but it has me confused.
I want to calculate the cross product of two vectors
a×r
The vectors are given by
a=az, r=xx+yy+zz
The vector r is the radius vector in cartesian coordinares.
I want to calculate the cross product in cylindrical coordinates, so I need to write r in this coordinate system.
The cross product in cartesian coordinates is
a×r=ayx+axy,
however how can we do this in cylindrical coordinates?

Answer & Explanation

Donald Proulx

Donald Proulx

Beginner2021-11-14Added 18 answers

The radius vector r in cylindrical coordinates is r=pp+zz. Calculating the cross-product is then just a matter of vector algebra:
a×r=az×(pp+zz)
=a(p(z×p)+z(z×z))
=ap(z×p)
=apϕ,
where in the last line we've used the orthonormality of the triad {p,ϕ,z}

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